Question

please answer it fast ​

Answer 1

Answer:

1a). 4/9+1/2=17/18

1b). 3/8+2/9=43/72

2a). 3/4-1/8=5/8

2b). 7/8-5/6=1/24

Answer 2

Q1. Evaluate:

a)  $\frac{4}{9} + \frac{1}{2}$

Step 1: Find the LCM of the denominators.

LCM of 9 and 2 is 18.

Step 2: Make the denominators equal.

$\frac{4\times 2 }{9\times 2 } + \frac{1\times 9 }{2\times 9 }$

$\frac{8}{18}+\frac{9}{18}$

Step 3: Add the numerators and let the denominator be the same.

$\frac{8}{18}+\frac{9}{18}$

$\frac{17}{18}$

$\bf \therefore \frac{4}{9} + \frac{1}{2} = \frac{17}{18}$

$\rule{300}{0.5}$

b)  $\frac{3}{8}+\frac{2}{9}$

Step 1: Find the LCM of the denominators.

LCM of 8 and 9 is 72.

Step 2: Make the denominators equal.

$\frac{3\times 9 }{8\times 9 }+\frac{2\times 8 }{9\times 8 }$

$\frac{18 }{72}+\frac{16 }{72 }$

Step 3: Add the numerators and let the denominator be the same.

$\frac{18 }{72}+\frac{16 }{72 }$

$\frac{34}{72}$

$\bf \therefore \frac{3}{8}+\frac{2}{9} = \frac{34}{72}$

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Q2. Evaluate:

a)  $\frac{3}{4}-\frac{1}{8}$

Step 1: Find the LCM of the denominators.

LCM of 4 and 8 is 8.

Step 2: Make the denominators equal.

$\frac{3\times 2 }{4\times 2 }-\frac{1}{8}$

$\frac{6 }{8}-\frac{1}{8}$

Step 3: Subtract the numerators and let the denominator be the same.

$\frac{6 }{8}-\frac{1}{8}$

$\frac{5 }{8}$

$\bf \therefore \frac{3}{4}-\frac{1}{8} = \frac{5}{8}$

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b) $\frac{7}{8}- \frac{5}{6}$

Step 1: Find the LCM of the denominators.

LCM of 8 and 6 is 24.

Step 2: Make the denominators equal.

$\frac{7\times 3 }{8\times 3 }- \frac{5\times 4 }{6\times 4 }$

$\frac{21}{24}- \frac{20}{2 4 }$

Step 3: Subtract the numerators and let the denominator be the same.

$\frac{21}{24}- \frac{20}{2 4 }$

$\frac{1}{24}$

$\bf \therefore \frac{7}{8}- \frac{5}{6} = \frac{1}{24}$

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Q3. Evaluate:

a) $\frac{2}{3} + \frac{5}{12} - \frac{3}{7}$

Step 1: Find the LCM of the denominators.

LCM of 3, 12 and 17 is 84

Step 2: Make the denominators equal.

$\frac{2\times 28 }{3\times 28 } + \frac{5\times 7 }{12\times 7 } - \frac{3\times 12 }{7\times 12 }$

$\frac{56 }{84} + \frac{35 }{84 } - \frac{36}{84}$

Step 3: Applying BOMDAS do addition first and then subtraction.

$\frac{56 }{84} + \frac{35 }{84 } - \frac{36}{84}$

$\frac{91 }{84} - \frac{36}{84}$

$\frac{55 }{84}$

$\bf \therefore \frac{2}{3} + \frac{5}{12} - \frac{3}{7} = \frac{55}{84}$

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Q4. Evaluate:

$7\frac{1}{3} + 2\frac{1}{5}$

Step 1: Convert the mixed fraction to improper fraction.

$\frac{7\times 3+1 }{3} + \frac{2\times 5+ 1}{5}$

$\frac{22 }{3} + \frac{11}{5}$

Step 2: Find the LCM of the denominators.

LCM of 3 and 5 is 15.

Step 3: Make the denominators equal.

$\frac{22\times 5 }{3\times 5 } + \frac{11\times 3 }{5\times 3 }$

$\frac{110 }{15 } + \frac{33 }{15}$

Step 4: Add the numerators and let the denominator be the same.

$\frac{110 }{15 } + \frac{33 }{15}$

$\frac{143}{15}$

$\bf \therefore 7\frac{1}{3} + 2\frac{1}{5} = \frac{143}{15}$

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Q5. Arrange in ascending order.

Step 1: Convert the mixed fraction into an improper fraction.

$4\frac{3}{4} = \frac{4\times 4+3}{4} = \frac{19}{4}$

Step 2: Find the LCM of all the denominators.

$\begin{array}{r | l} 2 & 8,9,10,4\\ \cline{2-2} 2 & 4,9,5,2 \\ \cline{2-2} 2& 2,9,5,1 \\ \cline{2-2} 3 & 1,9,5,1\\ \cline{2-2} & 1,3,5,1\ \end{array}$

LCM = 2×2×2×3×3×5 = 360

Step 3: Make the denominators equal.

$\frac{7\times 45 }{8\times 45 } = \frac{315}{360}$

$\frac{5\times 40 }{9\times 40 } = \frac{200}{360}$

$\frac{3\times 36 }{10\times 36 } = \frac{108}{360}$

$\frac{19\times 90 }{4\times 90 } = \frac{1710}{360}$

Step 4: Arrange the numbers in ascending form.

$\frac{108}{360} < \frac{200}{360} <\frac{315}{360} <\frac{1710}{360}$

$\frac{3}{10}<\frac{5}{9}<\frac{7}{8} < 4\frac{3}{4}$

$\bf \therefore \frac{3}{10}<\frac{5}{9}<\frac{7}{8} < 4\frac{3}{4}$

$\rule{300}{0.5}$